My T doesn't have any toys but I always have my fidget toy in my purse and I almost always play with it during the session. (I have a tangle toy that I play with so I can fidget quietly—it's not just for therapy).
It's actually not his office space during the day. He only practices in the evenings so it's another T's office during the morning/day. Idk if he would have toys if he set it up.

I think a good therapist should make every effort not to judge, but they're human. If they do judge, they should attempt not to show it. If it shows, they should be willing to talk it through with the client/patient.

I have no clue what breastfeeding means in this context? Like bringing an infant in to the session?